Even though your Principal Residence Exemption will not take effect until January of 2009, make sure that your exemption is filed with the taxing authority (city, village or township) as soon as you become the owner. This document should be part of the package you will sign at closing.
You will then be listed as the owner of the property on the city or township tax roles, and you can ask your mortgage company to contact them in January to get a correct estimate of your 2009 taxes, (for the calculation of the monthly amount you will be paying into your escrow for those taxes to be paid from next year). Request a Re-analysis of your escrow for taxes in January, and provide the contact information for your taxing authority to the mortgage co. person that will handle it.
If it is not homesteaded now, your escrow portion of your mortgage payment will be higher until you make sure it is changed, and generally, so will the 2 months or so advance escrow amount for taxes that the lender will add in at closing. It is Michigan law that you must file by May 1 to have the exemption for any year. Just be glad that you are not buying the home in June!
For additional information on Michigan property tax questions: